$88$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $47$ less than $2$ times the number of away team fans. How many home team and away team fans attended the game?
Answer: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 88}$ ${x = 2y-47}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${2y-47}$ for $x$ in the first equation. ${(2y-47)}{+ y = 88}$ Simplify and solve for $y$ $ 2y-47 + y = 88 $ $ 3y-47 = 88 $ $ 3y = 135 $ $ y = \dfrac{135}{3} $ ${y = 45}$ Now that you know ${y = 45}$ , plug it back into ${x = 2y-47}$ to find $x$ ${x = 2}{(45)}{ - 47}$ $x = 90 - 47$ ${x = 43}$ You can also plug ${y = 45}$ into ${x+y = 88}$ and get the same answer for $x$ ${x + }{(45)}{= 88}$ ${x = 43}$ There were $43$ home team fans and $45$ away team fans.